Answer:
Step-by-step explanation:
(a) Lett be the time (in days) since the start of the experiment, and let
y be the amount of the substance at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
y = ei
Answer: (a) The formula relating the amount of substance, y, to time, t, is given by:
y = y₀ * e^(-λ*t)
where y₀ is the initial amount of the substance, λ is the decay constant, and e is the mathematical constant approximately equal to 2.71828.
The half-life, T½, is related to the decay constant as:
T½ = ln(2)/λ
We are given that the half-life of the substance is 16 days, so we can solve for λ:
λ = ln(2)/T½ = ln(2)/16
Substituting this value of λ in the formula for y, we get:
y = 65.7 * e^(-ln(2)*t/16)
(b) To find the amount of substance present after 13 days, we substitute t = 13 in the formula for y:
y = 65.7 * e^(-ln(2)*13/16) ≈ 42.1
Rounding to the nearest tenth, we get y ≈ 42.1 g. Therefore, approximately 42.1 g of the substance will be present after 13 days.
Step-by-step explanation:
Suppose that the local government of Corpus Christi decides to institute a tax on soda consumers. Before the tax, 30 million liters of soda were sold every month at a price of $11 per liter. After the tax, 25 million liters of soda are sold every month; consumers pay $14 per liter (including the tax), and producers receive $6 per liter.
The amount of the tax on a liter of soda isper liter. Of this amount, the burden that falls on consumers isper liter, and the burden that falls on producers isper liter.
True or False: The effect of the tax on the quantity sold would have been larger if the tax had been levied on producers.
True
False
False. The effect of the tax on the quantity sold would not have been larger if the tax had been levied on producers.
What is Algebraic expression ?
An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It may contain one or more terms, with each term separated by a plus or minus sign. Algebraic expressions are used in algebra to represent mathematical relationships and formulas.
The tax incidence (the division of the burden of a tax between buyers and sellers) does not depend on which side of the market the tax is levied on, but rather on the relative elasticities of supply and demand. In this case, we don't have information about the elasticities of supply and demand, so we cannot determine the tax incidence. However, we can infer that the tax on consumers did reduce the quantity sold (from 30 million liters to 25 million liters), so it's unlikely that a tax on producers would have had a larger effect.
Therefore, False. The effect of the tax on the quantity sold would not have been larger if the tax had been levied on producers.
To learn more about Algebraic expression from given link.
https://brainly.com/question/31238826
#SPJ1
Write the linear equation that gives the rule for this table.
X
4
5
6
7
Y
24
30
36
42
Write your answer as an equation with y first, followed by an equals sign.
The equation of the line passing through the given points is y = 6x
Given that are the values of x and y coordinates we need to find the equation of the line using them,
So, considering the points (4, 24) and (5, 30),
We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Here (x₁, y₁) and (x₂, y₂) are (4, 24) and (5, 30),
Therefore, the required equation is =
y-24 = 30-24/5-4 (x-4)
y-24 = 6(x-4)
y-24 = 6x-24
y = 6x
Hence, the equation of the line passing through the given points is y = 6x
Learn more about equation of the line click;
https://brainly.com/question/21511618
#SPJ1
Ted made $56 in interest by placing $700 in a savings account with simple interest for 1 year. What was the interest rate?
The interest rate if Ted made $56 in interest for 1 year on a principle of $700 will be 8%.
Given, the interest amount is $56.
The principal amount is $700.
The time period of investment is 1 year.
Now, we have to find the interest rate.
The formula to find the simple interest is,
S.I = PTR/100.
Now, we need to substitute the values in the above formula.
S.I = PTR/100
56 = 700×1×R / 100
56 = 700R/100
5600 = 700R
R = 5600/700
R = 8
Therefore, the interest rate is 8%.
To know more about Simple Interest, click on:https://brainly.com/question/25845758
my bike tire has a radius of 12 inches how much distance will i cover after 50 rotations
Therefore , the solution of the given problem of unitary method comes out to be 50 tyre rotations, you will have covered around 376.99 inches (or about 31.41 feet).
What is a unitary method?The well-known simple approach, real variables, and any crucial elements from the very initial And specialised inquiry can all be used to finish the work. Customers may then be given another chance to try the product in response. If not, significant impacts on our understanding of algorithms will vanish.
Here,
The circumference of the circle the bike tyre forms is equal to the distance travelled in one rotation of the tyre. The following formula determines a circle's circumference:
=> C = 2πr
where the mathematical constant is roughly equivalent to 3.14159 and r is the circle's radius.
Your bicycle tyre's radius in this instance is 12 inches. The tyre's circumference is as follows:
=> C = 2π(12) = 24π inches
You may easily calculate how far you will travel after 50 spins by multiplying the tyre's circumference by the number of turns:
=> Covered distance: 50 × 24π ≈ 376.99 inches
As a result, after 50 tyre rotations, you will have covered around 376.99 inches (or about 31.41 feet).
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ9
A turtle lives in a garden and a hedgehog lives in the woods. They leave their homes at the same time, walk toward each other, and meet in 5 hours. The turtle walks 10 meters per hour slower than the hedgehog. It the turtle had left home 4.5 hours earlier than the hedgehog, the two have me 150/ from the hedgehog's house. Find the distance between the garden and the woods.
If a turtle lives in a garden and a hedgehog lives in the woods. The distance between the garden and the woods is 450m.
How to find the distance?Let d represent the distance between the turtle's garden and the hedgehog's wood
Let h represent the speed of the hedgehog
Let the turtle's speed = h-10
Le the time it takes for the hedgehog to walk from the woods to the meeting point= t
Set up two equations
d = (h-10)(t+4.5) + ht (Equation 1)
d - 150 = ht (Equation 2)
Solve for d by substituting equation 2 into equation 1:
ht + (h-10)(t+4.5) = ht + 150
(h-10)t + 45h = 150
t = (150 - 45h) / (h-10)
Substitute t into equation 2:
d = ht + 150 - (h-10)(t+4.5)
d = h(150 - 45h)/(h-10) + 150 - (h-10)(45h/(h-10) + 4.5)
d = 2250/(h-10) (distance between the garden and the woods)
Since the turtle and hedgehog meet in 5 hours
Thus,
d = ( h-10 ) (5) + h( 5- 4.5 )
d = 5h - 25
Substitute
5h - 25 = 2250/(h-10)
Multiplying both sides by h-10
5h² - 75h + 250 = 0
Dividing both sides by 5
h²- 15h + 50 = 0
Using the quadratic formula
h = (15 ± sqrt(15^2 - 4(1)(50))) / (2*1)
h = (15 ± 5) / 2
So,
h = 10 or h = 5
Distance between the garden and the woods :
d = 2250/(h-10)
d= 2250/(5-10)
= 450 meters
Therefore the distance is 450m.
Learn more about distance here:https://brainly.com/question/23594310
#SPJ1
1. A sample of 250 high-school students in a city results in an average number of text messages sent per month of 172.6, with a margin of error of + 4.8. If there are 3000 high-school students in the city, what is the estimated number of text messages sent in a month? between______ and____text messages
Answer:
Step-by-step explanation:
1) Find the upper bound of the confidence interval:
Upper bound = sample mean + margin of error
= 172.6 + 4.8
= 177.4
2) Find the lower bound of the confidence interval:
Lower bound = sample mean - margin of error
= 172.6 - 4.8
= 167.8
3) Estimate the total number of text messages sent in a month:
Total number of text messages sent = (number of students in the population / number of students in the sample) x sample mean
= (3000 / 250) x 172.6
= 2071.2
Therefore, the estimated number of text messages sent in a month is 2071.2, with a 95% confidence interval between 167.8 and 177.4 text messages.
Answer:
Between 503400 and 532200 text messages----------------------------
Determine the average number of text messages sent per student within the margin of errorFind lower bound:
172.6 - 4.8 = 167.8 text messagesFind upper bound:
172.6 + 4.8 = 177.4 text messages Estimate the total number of text messages for all 3000 studentsLower bound:
167.8 text messages × 3000 students = 503400 text messagesUpper bound:
177.4 text messages × 3000 students = 532200 text messagesThe estimated number of text messages sent in a month for all 3000 high-school students in the city is:
Between 503400 and 532200 text messagesCan someone help pleaseeee
The result of the row 1 multiplication by 1/4 is determined as [¹/₂ 0 ].
What is the result of the row multiplication?The resultant of the row multiplication in the Matrice is calculated by applying the following method;
row 1 in the given matrices = [2 0]
To multiply row by 1/4, we will multiply each entity by 1/4 as shown below;
[2 0] x 1/4 = 1/4(2 0)
= [¹/₂ 0 ]
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, that is 2, and 0 by 1/4.
Learn more about row multiplication here: https://brainly.com/question/31531585
#SPJ1
Solve and check: 3/4h+11=20 helpp!
Answer: 12
Step-by-step explanation:
We have to find h so the first step is to subtract the 11 from the 20
3/4h=9
Then to move the 3/4 over to the other side, you must multiply it by it's reciprocal, 4/3.
h= 4/3 x 9
This equals 12.
ACTIVITY 1: Find f−1 in each of the following.
The [tex]f^{-1}[/tex] inverse of f of each
1) (x + 1)/2
2) [tex]\sqrt{\frac{x+1}{4} } \\[/tex]
3) 3 - 4x
4) [tex](x+5)^{1/3}[/tex]
5) [tex]\sqrt{x + 4}[/tex]
1) function f(x) = 3x + 1
let f(x) = y
y = 3x + 1
y - 1 = 3x
(y - 1)/3 = x
x obtained is [tex]f^{-1}[/tex]
and y will be x
[tex]f^{-1}[/tex] = (x-1)/3
2) equation f(x) = 4x² - 1
let f(x) = y
y = 4x² - 1
y + 1 = 4x²
(y + 1 )/4 = x²
x = [tex]\sqrt{\frac{x + 1}{4} }[/tex]
x obtained is [tex]f^{-1}[/tex]
and y will be x
[tex]f^{-1}[/tex] = [tex]\sqrt{\frac{x + 1}{4} }[/tex]
similarly,
3) f(x) = 3-x/4
y = 3-x/4
4y = 3 - x
x = 3 - 4x
[tex]f^{-1}[/tex] = 3- 4x
4) y = x³ - 5
y + 5 = x³
x = [tex](y + 5)^{1/3}[/tex]
[tex]f^{-1}[/tex] = [tex](x+5)^{1/3}[/tex]
5) y = x² - 4
y + 4 = x²
x = √y + 4
[tex]f^{-1} = \sqrt{x + 4}[/tex]
To know more about inverse click here :
https://brainly.com/question/26257987
#SPJ1
According to the graph, what is the maximum number of passengers he can transport What is the maximum amount he can collect? Use the graph to determine the amount he charges a single passenger.
I can't see the chart...
Please help quickly I'm begging!
Assignment details: In this assignment, you will create two graphs and answer questions about Bond's Gym, the business you are supporting.
The functions are f(x) = 600 - 10x & g(x) = 20/3x, and the graphs are added as attachments
Creating the functions of the Bond's GymFrom the question, we have the following parameters that can be used in our computation:
The table of values
For the membership application, we have the following features
Initial value = 600Constant rate of change = (450 - 600)/(15 - 0) = -10So, the function is
f(x) = 600 - 10x
For the membership available, we have the following features
Initial value = 0Constant rate of change = (100 - 0)/(15 - 0) = 20/3So, the function is
g(x) = 20/3x
So, the functions are f(x) = 600 - 10x & g(x) = 20/3x
Read more about linear relation at
https://brainly.com/question/30318449
#SPJ1
3 problems for 1 final answer. fairly easy 8th grade math.
When we evaluate the given expression, A/5 + √(B - C), the result obtained is 9 (option B)
How do i determine the value of A/5 + √(B - C)?
First, we shall determine the value of A. Details below:
A = Product of roots in x² - 11x + 30Value of A =?Quadratic equation is expressed as:
x² - (sum of root)x + product of root
Comparing the above with x² - 11x + 30, we have
x² - 11x + 30 = x² - (sumof root)x + product of root
Product of roots = 30
Thus,
A = 30
Next, we shall determine the value of B. details below:
f(x) = x² + 5Value of B = f(2) =?f(x) = x² + 5
f(2) = 2² + 5
f(2) = 9
Thus,
B = 9
Next, we shall determine the value of C. Details below:
(x² - 2x - 24) / (x + 4)Value of C = Remainder =?Let
x + 4 = 0
Thus,
x = -4
Substitute the value of x into x² - 2x - 24 to obtain the remainder as shown below:
Remainder = x² - 2x - 24
Remainder = (-4)² - 2(-4) - 24
Remainder = 0
Thus,
C = 0
Finally, we shall determine value of A/5 + √(B - C). Details below:
A = 30B = 9C = 0Value of A/5 + √(B - C) =?A/5 + √(B - C) = 30/5 + √(9 - 0)
A/5 + √(B - C) = 6 + √(9
A/5 + √(B - C) = 6 + 3
A/5 + √(B - C) = 9
Thus, the value of A/5 + √(B - C) is 9 (option B)
Learn more about algebraic expression:
https://brainly.com/question/12518138
#SPJ1
In circle
V
V,
V
W
=
2
VW=2 and the length of
⌢
=
2
9
π
WX
⌢
=
9
2
π. Find m
∠
W
V
X
∠WVX.
Answer:
Step-by-step explanation:
In a circle, the measure of an inscribed angle is equal to half the measure of its intercepted arc. In this case, the inscribed angle is ∠WVX and its intercepted arc is ⌢WX.
Since the length of ⌢WX is (9/2)π, its measure in degrees is (9/2)π * (180/π) = 810/2 = 405 degrees.
Therefore, the measure of ∠WVX is half the measure of its intercepted arc, which is 405/2 = 202.5 degrees.
PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
A. Using the formula for area of rectangle, the length of the rectangular space is: 2x - 3
B. The expression to prove this is: (2x - 3) * 4x = 8x² - 12x
What is the Area of a Rectangle?To find the area of a rectangle, multiply the width and the length together. This means: Area = length * width.
Part A: We are given that area of the rectangular space is expressed as 8x² - 12x, if the width is 4x, then:
Length of the rectangular space = (8x² - 12x) / 4x = 4x(2x - 3)/4x
Length = 2x - 3
Part B: To prove this, we have:
length * width = 8x² - 12x
Substitute:
(2x - 3) * 4x = 8x² - 12x
Learn more about area of rectangle on:
https://brainly.com/question/29604954
#SPJ1
Unit seven geometry and measurement homework to perimeter area of rectangles and parallelograms answer key
The required maximum area of the rectangle is 17.5m
How to explain the perimeterThe perimeter of a rectangle is = 70m.
We have to find The maximum area of rectangle .
A rectangle will have the maximum possible area for a given perimeter when all the sides are the same length. Since every rectangle has four sides, if you know the perimeter, divide it by four.
Maximum area of rectangle is = 70 / 4
= 17.5
The required value of maximum area of the rectangle is 17.5m.
Learn more about Perimeter on
https://brainly.com/question/19819849
#SPJ1
the perimeter of a rectangle is 70m. What are the dimensions that will produce the maximum area of such a rectangle
HELP ASAP PLEASE 20 POINTS!!
The calculated value of the surface area of the cylinder is 138π square inches
Calculating the surface area of the cylinderFrom the question, we have the following parameters that can be used in our computation:
Height, h = 5 1/2 inches
Diameter, d = 12 inches
Using the above as a guide, we have the following:
SA = 2πr(r + h)
Where
Radius, r = d/2
r = 12/2
r = 6
Substitute the known values in the above equation, so, we have the following representation
SA = 2 * π * 6(6 + 5 1/2)
Evaluate
SA = 138π
Hence, the surface area of the cylinder is 138π square inches
Read more about surface area at
brainly.com/question/16519513
#SPJ1
What is the equation through the points: (-7, -3), (1, 2)
ASAP please
The equation of the line passing through the points (-7, -3) and (1, 2) is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].
What is the equation of the line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
First, we determine the slope of the line.
Given the two points are (-7, -3) and (1, 2)
We can find the slope of the line by using the slope formula:
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values, we get:
m = (2 - (-3)) / (1 - (-7))
m = 5/8
Using the point-slope form, plug in one of the given points and slope m = 5/8 to find the equation of the line.
Let's use the point (-7, -3:
y - y₁ = m(x - x₁)
[tex]y - (-3) = \frac{5}{8}( x - (-7) ) \\\\y + 3 = \frac{5}{8}(x + 7 )\\\\y + 3 = \frac{5}{8}x + \frac{35}{8} \\ \\y = \frac{5}{8}x + \frac{35}{8} - 3\\\\y = \frac{5}{8}x + \frac{11}{8}[/tex]
Therefore, the equation of the line is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].
Learn more about equation of line here: brainly.com/question/2564656
#SPJ1
Draw n equally spaced marks between 0 and 1 on each of the x and y axes. Connect the first mark on the x-axis (closest to 0) to the last mark on the y axis (closest to 1), the second mark on the x axis to the second last on the y axis, and so on.
As n increases this process creates a curved boundary, C, as seen in this example diagram. Give an equation for this curve as n → ∞.
the equation for the curve C as n approaches infinity is y = x This is the equation of the diagonal line that passes through the points (0, 0) and (1, 1).
what is diagonal line ?
A diagonal line is a straight line that runs obliquely (at an angle) between two opposite corners of a geometric shape, such as a rectangle or a square. It is called "diagonal" because it connects two non-adjacent vertices of the shape, forming a diagonal across the interior of the shape.
In the given question,
As n increases, the process described in the question creates a set of line segments that connect the equally spaced points on the x-axis to the equally spaced points on the y-axis. The resulting curve is a piecewise linear function that converges to a continuous curve as n approaches infinity.
To derive an equation for this curve, we can start by considering the line segment connecting the first mark on the x-axis to the last mark on the y-axis. Let's call this point (0, 1) and the nth mark on the x-axis (1, 0). The slope of the line connecting these two points is given by:
m = (0 - 1) / (1 - nth mark) = (1 - nth mark)^(-1)
where the nth mark on the x-axis is given by:
nth mark = 1 - (1/n)
Substituting this expression for nth mark into the equation for m, we get:
m = (n/(n-1))
The y-intercept of the line is given by:
b = 1 - m = 1 - (n/(n-1)) = 1/(n-1)
Therefore, the equation for the line segment connecting the first mark on the x-axis to the last mark on the y-axis is:
y = (n/(n-1))x + 1/(n-1)
Similarly, the equation for the line segment connecting the second mark on the x-axis to the second last on the y-axis is:
y = (n/(n-2))x + 1/(n-2)
Continuing this process for all n line segments, we get:
y = (n/(n-k))x + 1/(n-k)
where k = 1, 2, ..., n.
To get the equation for the curve C, we need to take the limit as n approaches infinity. As n goes to infinity, the value of k becomes insignificant compared to n, and we can approximate the equation for the curve as:
y = x
Therefore, the equation for the curve C as n approaches infinity is:
y = x
This is the equation of the diagonal line that passes through the points (0, 0) and (1, 1).
To know more about diagonal line , visit:
https://brainly.com/question/9253179?
#SPJ1
Please help me out with this
Answesar:
Step-by-step explanation:
SA = 10(5)² = 250cm²
Volume² = 2 (5)³ = 250cm³
They are not equal.
Surface area is in square cm and volume is in cm³.
HELP PLEASE I REALLY NEED HELP ON THIS QUESTION HELP!
The number for which the theoretical probability matches the experimental probability is 2.
What is experimental and theoretical probability?
Experimental probability and theoretical probability are two different ways to determine the likelihood of an event occurring.
Experimental probability is determined by performing an experiment or conducting observations and collecting data to see how often an event occurs. This method involves counting the number of times an event occurs and dividing that number by the total number of trials or observations.
Theoretical probability, on the other hand, is determined by using mathematical principles and calculations to determine the likelihood of an event occurring. It is based on the assumption that all outcomes are equally likely.
In the given table;
For theoretical, P(2) = 1/4
For experimental, P(7) = 7/28 = 1/4
Learn more about experimental probability here: https://brainly.com/question/8652467
#SPJ1
in the diagram below A, B, C are points in the same horizontal plane with AC =BC=22.3 meters.AD is a vertical tower which is anchored at B and C.The angle of elevation of D from B is 25.4. BDC=58.6 and ACB= 50.8.
The length of AB is 27.3m and AD is 113 m.
Using Trigonometry in Triangle ABC
tan 50. 8 = P / B
tan 50.8 = AB / 22.3
1.2261 = AB/ 22.3
AB = 27.34 m
Now, again using Trigonometry
tan 25.4 = P / B
tan 50.8 = AD / 27.34
0.474 = AD/ 27.34
AD = 12.95916 m
Learn more about Trigonometry here:
https://brainly.com/question/29002217
#SPJ1
How do I solve this?
The 99% confidence interval estimate of the population standard deviation is [12.54, 54.62] mi/h.
What is a confidence interval?A confidence interval is the mean of your estimate plus and minus the variation in that estimate. This is the range of values you expect your estimate to fall between if you redo your test.
x = [64, 60, 56, 60, 52, 59, 58, 59, 70, 68]
s = 5.963
n = 10
CI = [(n-1)*s²/chi2_upper, (n-1)*s²/chi2 lower]
CI = [(9*5.963^m²)/19.022, (9*5.963²)/2.700]
CI = [12.54, 54.62]
Learn more about interval on
https://brainly.com/question/15712887
#SPJ1
Ellie and her older brother, Shawn, just got new phones! Both phones are shaped like rectangular prisms that are 3/4 of a centimeter tall. Ellie went with the smaller model that is 12 centimeters long and 6 centimeters wide, while Shawn went with the larger model that is 15 centimeters long and 8 centimeters wide. How many cubic centimeters larger is Shawn's phone than Ellie's?
Shawn's phone is 36 cubic cm larger than Ellie's phone.
How many cubic cm larger is Shawn's phone?To get difference in volume between the two phones, we must calculate volume of each phone and subtract the volume of Ellie's phone from the volume of Shawn's phone.
The volume of a rectangular prism is: length*width* height. The height of both phones is 3/4 centimeters.
The volume of Ellie's phone is:
= length x width x height
= 12 cm x 6 cm x (3/4) cm
= 54 cubic centimeters
The volume of Shawn's phone is:
= length x width x height
= 15 cm x 8 cm x (3/4) cm
= 90 cubic centimeters
The difference in volume is:
= Volume of Shawn's phone - Volume of Ellie's phone
= 90 cubic centimeters - 54 cubic centimeters
= 36 cubic centimeters
Read more about volume
brainly.com/question/27710307
#SPJ1
ACTIVITY 1: Complete the table below by computing the unknown component of simple interest.
Answer:
what arecrosses on line 2
The approximate number of zombies in a certain city over time is given in the table below. Answer the questions below to determine what kind of function would best fit the data, linear or exponential.
Number of Hours Since Zombies First Spotted, x
1
2
3
4
Approximate Number of Zombies, f(x)
24
56
88
122
function would best fit the data because as x increases, the y values change
. Rounded to the nearest .5, the
of this function is approximately
A linear function would be the best fit for the given data because as x increase the y-values change linearly.
Rounded to the .5 the slope of the function is approximately 32.5
Which type of function models the population?A linear relation means that any increase of 1 unit in the independent variable (x) has always the same impact in the other variable (y).
In this particular case, the increases in the y-value are:
56 - 24 = 32
88 - 56 = 32
122 - 88 = 34
The mean of that, rounded to .5, is (32 + 32 + 34)/3 = 32.5
So the change is almost the same one, then this seems to be a linear relation.
Learn more about linear relations at:
https://brainly.com/question/13828699
#SPJ1
Can someone help me with this please
Answer:
36 °
Step-by-step explanation:
The markings imply equal sides*
So both of the angles are 27° there
To find angle a we do 180 - (27+27) and obtain 126°
Then to find angle y, we do 180-angle a which is 180-126 and we get 54°
We now have reached the triangle where you're supposed to find x right?
So x is equal to 180 - both other angles, which is 180 - (90 and angle y) = 180- (90+54) = 180 - 144 = 36 which is your final answer
A system of equations is shown.
{ x= = 10
3x + 5y = 20
What is the solution x of the system of equations?
Answer:
(r, y)=(10,-2)
Step-by-step explanation: Hope this helps :)
Use the quadratic formula to solve -2x^2+2x+1
The solutions for -2x²+2x+1 are x = 1 + √(3)/2 and x = 1 - √(3)/2.
To use the quadratic formula to solve -2x²+2x+1, we first identify the coefficients a, b, and c of the quadratic equation in standard form: ax²+bx+c=0. In this case, a=-2, b=2, and c=1. We then plug these values into the quadratic formula
x = (-b ± √(b²-4ac)) / 2a
Substituting the values, we get
x = (-2 ± √(2²-4(-2)(1))) / 2(-2)
Simplifying the expression inside the square root
x = (-2 ± √(4+8)) / (-4)
x = (-2 ± √12) / (-4)
Simplifying the radical
x = (-2 ± 2√3) / (-4)
Reducing the fraction
x = (1 ± √3/2)
Therefore, the two solutions are x = (1 + √3/2) and x = (1 - √3/2).
To know more about quadratic formula:
https://brainly.com/question/9300679
#SPJ1
What is an equation of the line that passes through the point (5,-5)(5,−5) and is parallel to the line x+5y=20?
Answer:
[tex]y = -x/5 -4.[/tex]
Step-by-step explanation:
To simplify the line x + 5y = 20 into y = mx + b form:
x + 5y = 20.
5y = -x + 20.
y = -x/5 + 4.
The line parallel to the line y = -x/5 + 4 will have the same slope of -1/5.
We get the equation:
y = -x/5 + b.
To find b, we plug in the point (5, -5).
-5 = -5/5 + b.
-5 = -1 + b.
b = -4.
[tex]y = -x/5 -4.[/tex]
How do you find area?
The area of a shape is calculated by calculating the amount of space on the shape
How do you find area?By definitinon, the area of a shape is the amount of space on the shape
using the above as a guide, we have the following:
Area of rectangle = Length * WidthArea of square = Length²Area of triangle = 1/2 * base * heightArea of circle = π * radius²Area of parallelogram = base * heightThere are several formulas to calculate area
The formula to use is dependent on the shape whose area is being calculated
This means that the area of trapezoid cannot be calculated using the area of parallelogram
Read more about area at
https://brainly.com/question/24487155
#SPJ1